% displacementexcitedstring.m Last modified 8/4/2008 % String driven at the left end with known sinusoidal displacement % with amplitude Y0 and fixed at the right end. Input is the ratio of the % forcing frequency to the first natural frequency. clear all set(0,'DefaultAxesFontSize',12); set(0,'DefaultTextFontSize',12); fratio=-1; while fratio<=0|fratio==1|fratio==2|fratio==3 disp(' '); string1=' The ratio of excitation freq. to first natural freq. = '; fratio=input(string1); if fratio==1|fratio==2|fratio==3 disp(' ') disp(' This is the resonant case choose another freq. ratio'); disp(' ') end disp(' '); end xoverL=linspace(0,1,201); sw=cos(fratio*pi*xoverL)-(sin(fratio*pi*xoverL)/tan(fratio*pi)); lim=max(abs(sw)); figure(1);clf; axis([0 1 -.2*lim 1.2*lim]); hold on plot(xoverL,abs(sw)) hold on plot([0 1],[0 0]); text(.8,1.1*lim,['f/f_1 = ',num2str(fratio)]) xlabel('Dimensionless distance from the fixed end, x/L') ylabel('Dimensionless Amplitude, y(x)/Y_0') text(.1,1.1*lim,'Press Enter to Continue') hold off xp1=.5+.5*[1 1 1.1 1.3 1.2 1.32 1.2 1 1]; yp1=1.5*lim*[0 .4 .3 .2 .1 0 -.2 -.4 0]; pause xbox=[-.2 -.2 0 0 -.2]; ybox=[-.5 .5 .5 -.5 -.5]; figure(2);clf; set(gca,'Box','on') axis([-.3 1.3 -2*lim 2*lim]); hold on patch(xp1,yp1,'r') xlabel('Distance, x/L') ylabel('Displacement, y(x,t)/Y_0') hold on x1=[-.3 1];y1=[0 0]; plot(x1,y1) hold on texthandle2=text(-.1,-1.6*lim,['f/f_1 = ',num2str(fratio)]); ys=sw*0; plot(xoverL,ys,'k','LineWidth',[1.5]); base=plot(xbox,ybox,'r','EraseMode','xor'); ydata=[ys]; texthandle2=text(0,1.5*lim,'Press Enter to Animate one Frame at a Time'); xlabel('Distance , x/L'); ylabel('Displacement, y(x,t)/Y_0'); pause t=linspace(0,8*pi,257); sine=sin(t); for k=1:2:65 ys=sw*sine(1,k); plot(xoverL, ys,'k','LineWidth',[1.5]); hold on set(base,'Ydata' ,ybox+sine(1,k*ones(1,5))); hold on set(texthandle2,'String', 'Press Enter to Animate One Frame at a Time'); if k==65 set(texthandle2,'String', 'Press Enter to Continue '); end pause end hold off figure(3);clf; set(gca,'Box','on') axis([-.3 1.3 -2*lim 2*lim]); hold on patch(xp1,yp1,'r') xlabel('Distance, x/L') ylabel('Displacement, y(x,t)/Y_0') hold on x1=[-.3 1];y1=[0 0]; plot(x1,y1) hold on texthandle2=text(-.1,-1.6*lim,['f/f_1 = ',num2str(fratio)]); ys=sw*0; L=plot(xoverL,ys,'k','EraseMode','xor','LineWidth',[2.5]); ydata=[ys]; base=plot(xbox,ybox,'r','EraseMode','xor'); texthandl=text(0,1.5*lim,'Press Enter to Animate'); xlabel('Distance , x/L') ylabel('Displacement, y(x,t)/Y_0') pause set(texthandl,'String',' '); t=linspace(0,8*pi,257); sine=sin(t); for k=2:257 ys=sw*sine(1,k);; set(L,'Ydata',ys) set(base, 'Ydata',ybox+sine(1,k)*ones(1,5)); pause(.05) ydata=[ydata ;ys]; end set(texthandl,'String','Press Enter to Continue'); hold off pause figure(4);clf; [X,T]=meshgrid(xoverL,t); mesh(X,T,ydata) axis([0 1 0 8*pi -1.2*lim 1.2*lim]); text(1,5,-lim,'Dimensionless Time, \omegat','Rotation',-10) text(1,25,-lim,'Dimensionless Distance, x/L','Rotation',32) zlabel('Displacement, y(x,t)/Y_0') text(0,4,1.1*lim,'Press Enter to Continue','Rotation',-10) view(120,30) pause